Logit Lab material borrowed from tutorial by William B Logit Lab material borrowed from tutorial by William B. King Coastal Carolina see: ww2.coastal.edu/kingw/statistics/R-tutorials/logistic.html

# Start by loading MASS library # Note: Functions and datasets to support Venables and Ripley, 'Modern Applied Statistics with S’ library("MASS") #Load data set for analysis data(menarche) #View structure of data str(menarche)

# There are 3 variables with 25 observations: Age: average age of each cohort, i.e., partitioned by age Total: total number of girls in each cohort Menarche: number of girls that have reached menarche # Get summary statistics summary(menarche) # See ranges for each variable along with distributions info

# Plot data plot(Menarche/Total ~ Age, data=menarche) # Wow # Plot data plot(Menarche/Total ~ Age, data=menarche) # Wow! Looks like a really good data set for logistic regression # What does the logistic regression command look like? glm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche) # So what is glm? ?glm # we see that this is a generalized linear model function.

# Lets parse the command glm # Lets parse the command glm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche) # glm – generalized linear model # What is cbind(Menarche, Total-Menarche) ~ Age? # Type in cbind(Menarche, Total-Menarche) # Why do you get an error?

# You get an error because Menarche & Total are variables in a frame and # not top-level variables. # Recall the plot command we used: plot(Menarche/Total ~ Age, data=menarche) # Notice: data = menarche. This specifies the data frame # this is equivalent to plot(menarche$Menarche/menarche$Total ~ menarche$Age)

# What is cbind(Menarche, Total-Menarche) # What is cbind(Menarche, Total-Menarche)? # when data=menarche, cbind(Menarche, Total-Menarche) is # cbind(menarche$Menarche, menarche$Total-menarche$Menarche) # Type it in cbind(menarche$Menarche, menarche$Total-menarche$Menarche) # We see that these are the Y values of the points representing the dichotomy # Thus cbind(Menarche, Total-Menarche) ~ Age, # are the Y ~ X values that are arguments to the model # What about family=binomial(logit)? # This tells the glm function to fit the data using the logit model

# Altogether glm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche) # Ok, let’s examine the result of fitting the data with the logit model plot(Menarche/Total ~ Age, data=menarche) lines(menarche$Age, glm.out$fitted, type="l", col="red") title(main="Menarche Data with Fitted Logistic Regression Line") #Good fit!!!

# Check the statistics summary(glm # Check the statistics summary(glm.out) # Observe that the Estimated coefficient of Age is 1.63197 # Recall that the response variable is log odds so # so the change in odds is exp(1.632) = 5.11 times. # Interpretation: for every year increase in age the odds of having reached # menarche increase by exp(1.632) = 5.11 times.